I don't believe it can work with MBAM malicious websites function, as the SafeZone (including its custom browser) is isolated from the normal desktop.
The point at which MBAM malicious websites would get involved if you tried to connect to a malicious website using your normal browser. I say this as I believe MBAM isn't acting like a firewall which would intercept connections outside of your normal browser.
Personally I feel that the MBAM malicious websites function is its worst aspect, as it doesn't do what it says on the tin, only block malicious websites. It blocks much more than malicious websites, other categories unrelated to being malicious websites. Generally I turn that feature off, but a few version updates ago, doing that resulted in the tray icon changing to a grey icon.